Week 1 Assignment 1

1. True or false. The slope of a horizontal line is undefined.

True. Take any two distinct points on the line (x1,y1),(x2,y2). The slope is (y2-y1)/(x2-x1). Since the line is horizontal, the y values will be the same and since the points are distinct, the x values will note. Thus, the numerator is 0 and the denominator is non-zero and the slope is thus always zero.

2. True or false. Suppose the slope of a straight line L is -3/4 and P is a given point on L. If Q is a point on L lying 2 units to the right of P, then Q is situated 3/2 units below P.

True. The slope of our line is -3/4.

y=mx+b

y=-3/4x (b is irrelevant in our case)

So if we define our point, P, as being x=1 on our graph, y will equal -3/4

y=-3/4(1)

Now we need to define Q. Q is 2 units away from P. P = 1 so Q = 3

Lets plug in for Q:

y=-3/4(3)

y=-9/4

(-3/4) - (-9/4)

-3/4 + 9/4

6/4

3/2 or 1.5

3. True or false. The y-intercept of the straight line with equation Ax + By + C = 0 is –CIB (B 1 0).

True.

The y-intercept of the straight line with equation Ax + By + C = 0 is -C/B (B ¹ 0). *

to get y intercept, put x =0

By+C = 0

y = -C/B

4. True or false. If a line L1 has equation y = mx + b, where m and b are constants with m 1 0, then an equations of a line L2 perpendicular to L1 has the form y = -1/m x + C. where C is a constant.

True.

5. True or false. Suppose an asset is being depreciated linearly. Then the rate of depreciation of the asset is given by the negative of the slope of the depreciated line.

True. The depreciation line will have a negative slope which is the rate at which the value is decreasing and the rate of depreciation is just the negative of that value.

6. True or false. If R and C are linear revenue and cost functions, respectively, and (X0, P0) is the breakeven point, then P(x) > P(X0) if X > X0, where P is the profit function.

True. Increasing production from the breakeven points yields greater profits from linear...